NUMERICAL SIMULATION OF THE TUNGSTEN INERT GAS PROCESS. ul. Mikołajczyka 5, Opole 2, 3 Silesian University of Technology

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1 24/4 Archivs o Foundry, Yar 22, Volum 2, 4 Archiwum Odlwnictwa, Rok 22, Rocznik 2, Nr 4 PAN Katowic PL ISSN NUMERICAL SIMULATION OF THE TUNGSTEN INERT GAS PROCESS A. NOWAK 1, A. POCICA 2 E. MAJCHRZAK 3, M. DZIEWOŃSKI 4 1, 2 Tchnical Univrsity o Opol ul. Mikołajczyka 5, Opol 2, 3 Silsian Univrsity o Tchnology ul. Konarskigo 18a, 44-1 Gliwic SUMMARY In th papr th numrical modl o hat tratmnt o th casting supricial layr using th TIG mthod is prsntd. Th xtrnal hat sourc shits with a constant rat. Its inlunc on th casting surac causs th ct o th hat tratmnt. Such tchnology is calld th tungstn inrt gas procss. In th rgion o hat sourc action on can obsrv th partial mlting o th supricial layr. In th papr th 3D problm is analyzd. Th thrmal procsss in th domain considrd ar dscribd by th nrgy quation writtn in th orm corrsponding to th on domain mthod. Th inlunc o xtrnal hat sourc is substitutd by th Numann boundary condition. Th problm has bn solvd using th init dirnc mthod and th rsults hav bn compard with th solution obtaind by mans o th commrcial cod MARC/MENTAT. It turnd out that th rsults ar practically th sam. Thy will b prsntd in th inal part o th papr. ky words: numrical simulation, solidiication, tungstn inrt gas procss. 1. GOVERNING EQUATIONS W considr th 3D objct orintd in Cartsian co-ordinat systm. Th thrmal procsss procding in this domain (w assum only conductional hat transr) ar 1 dr inż. 2 dr inż. 3 pro.dr hab.inż., maj@zus.polsl.gliwic.pl 4 dr inż., mirk@rmt4.kmt.polsl.gliwic.pl

2 187 dscribd by th ollowing nrgy quation: T T T T c = λ + λ + λ + qvm t x x y y z z (1) m whr c=c(t ) is th volumtric spciic hat, λ=λ(t ) is th thrmal conductivity, q V (m) ar th capacitis od intrnal hat sourcs, in particular q Vm = L ( m) V ( m) S t whr L V (m) ar th latnt hats corrsponding solidiying phas (in th cas o cast iron m = 1 idntiis th austnit and m = 2 th utctic phass), S (m) ar th solid stat ractions o ths phass at th nighborhood o th point considrd. W assum that th succssiv phas changs procd on atr th othr and w introduc to th considrations th substitut thrmal capacity dind as th drivativ o nthalpy unction H with rspct to tmpratur (th on domain approach [1]). In this way th quation (2) taks a orm T T T T C( T ) = λ + λ + λ t x x y y z z whr C(T )=dh(t )dt. Th cours o nthalpy unction or th matrial considrd is prsntd in [2]. Bcaus o th discontinuity o nthalpy unction or th utctic tmpratur T u, th ral cours o H (T ) must b substitutd by th continuous unction or which th paramtr C(T ) can b dind. In this plac w us th zro ordr smoothing procdur introducing th crtain intrval [T u - T, T u + T] - as in [2]. In this way th substitut thrmal capacity o cast iron is dtrmind by th pic-wis constant unction. So, th unction C (T ) is dind as ollows cs T < T u T cu Tu T T < Tu + T C( T ) = c aus T u + T T < T L cl T TL whr T L is th liquidus tmpratur. Th valus o c S, c u, c aus and c L corrspond to slops o straight lins bing th approximation o nthalpy-tmpratur diagram [2]. Th ollowing boundary-initial conditions supplmnt th mathmatical modl o th procss: or th rgion o casting surac subjctd to th xtrnal hat sourc (Fig. 1) ( ) q ( ) λ T x, y, z, t n = x, y, z, t (5) / b (2) (3) (4)

3 188 whr q b is th known boundary hat lux, whil T/ n is th normal drivativ, on th rmaining part o th casting surac (,,, ) T x y z t λ = α( T) T( x, y, z, t) T n whr α(t ) is th hat transr coicint, T is th ambint tmpratur, or tim t = ( ) ( T xyz,,, = T xyz),, (7) whr T is th initial tmpratur. (6) Fig. 1. Th domain considrd Rys. 1. Rozpatrywany obszar Th intraction o xtrnal hat sourc which thrmal powr is qual to Q has bn assumd in th orm o th 2D Gauss distribution. Th paramtrs o th unction has bn it in this way in ordr to assur th mission o.95q on th surac o radius R - Figur 2. Fig.2. Function (x, y, ) Rys.2. Funkcja (x, y, )

4 THE METHOD OF SOLUTION In ordr to solv th problm abov discussd th init dirnc mthod has bn usd. Th domain has bn covrd by th rctangular msh. Th points rsulting rom th discrtization corrspond to th nods or which th unknown tmpraturs ar sarchd. Th FDM algorithm (an xplicit schm) has bn constructd in th orm dscribd in [3, 4]. Th FDM approximation o th quation (3) is o th orm + 1 ( ) T T T T C = 6 F (8) t = 1 R whr C is th spciic hat o cntral nod, R ar th thrmal rsistancs btwn nod considrd '' and th adjacnt ons '' ( = 1, 2,..., 6), F =1/ h ar th shap unctions, h is th msh stp, t= t +1 -t is th tim stp,, +1 ar th two succssiv tim lvls. Th thrmal rsistanc R ar dind as ollows [3, 4] R =.5h.5h λ + λ (9) whil in th cas o boundary nods (in th dirction o xtrnal boundary) R.5h 1 = + (1) λ α ( T, T ) Finally th quation (8) taks a orm whr T = AT = (11) 6 F t A =, = 1, K,6, A = 1 A (12) C R = 1 Th condition o dirntial schm stability rducs to A > or ach grid point. 3. THE RESULTS OF COMPUTATIONS Th cubicoid o dimnsions [mm] has bn analyzd. Along th axis o symmtry o uppr wall th xtrnal hat sourc movs with a constant rat

5 19 v = 1 [mm/min]. Arc voltag U = 13 [V], wlding currnt I = 7 [A], thrmal icincy η [.4,.65] [5]. Th thrmophysical paramtrs o th matrial can b ound in [6]. Figur 3 shows th tmpratur distribution in th domain considrd. Fig.3. Tmpratur distribution ( t = 6, 12 sc.) Rys.3. Rozkład tmpratury ( t = 6, 12 sc.)

6 191 REFERENCES [1] E.Majchrzak, B.Mochnacki, Application o th BEM in th thrmal thory o oundry procsss, Eng. Anal. with BEM, 16, (1995). [2] J.Szargut, Oblicznia cipln piców przmysłowych, Śląsk, Katowic, [3] B.Mochnacki, J.S.Suchy: Numrical mthods in computations o oundry procsss, PFTA, Cracow, [4] E. Saatdjian, Transport phnomna. Equations and numrical solutions, J.Wily & Sons, Chichstr, Nw York, 2. [5] J.F.Lancastr (d.), Th physics o wlding, Prgamon Prss, Oxord, Nw York, [6] B.Mochnacki, A.Nowak, A.Pocica, Numrical modl o supricial layr hat tratmnt using th TIG mthod, Polska Mtalurgia w Latach , Rd. K.Świątkowski, Komitt Mtalurgii PAN, Tom 2, (22). STRESZCZENIE SYMULACJA NUMERYCZNA PROCESU TIG W pracy przdstawiono modl numryczny obróbki powirzchni odlwu mtodą TIG. Zwnętrzn źródło cipła przmiszcza się ponad powirzchnią odlwu z stałą prędkością. Jgo oddziaływani na powirzchnię daj kt obróbki ciplnj. W rjoni oddziaływania źródła można zaobsrwować siln nagrzani i nadtopini warstwy wirzchnij odlwu. W pracy rozważano problm przstrznny (3D). Zadani opisuj równani Fourira-Kirchhoa (zapisan w konwncji mtody jdngo obszaru) uzupłnion odpowidnimi warunkami jdnoznaczności. Wpływ źródła zwnętrzngo zastąpiono warunkim brzgowym Numanna. Problm rozwiązano mtodą różnic skończonych, a wyniki porównano z rozwiązanim uzyskanym przy wykorzystaniu programu narzędziowgo MARC/MENTAT. Okazało się, ż rozwiązania są z praktyczngo punktu widznia taki sam. W końcowj części pracy przdstawiono wyniki symulacji numrycznych. Rcnzował Pro. Bohdan Mochnacki

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